The class of generalized lambda distributions (GLDs) is primarily used for modeling univariate real-world data. The GLD has not been as popular as some other methods for simulating observations from multivariate distributions because of computational difficulties. In view of this, the methodology and algorithms are presented for extending the GLD from univariate to multivariate data generation with an emphasis on reducing computational difficulties. Algorithms written in Mathematica 5.1 and Fortran 77 are provided for implementing the procedure and are available from the authors. A numerical example is provided and a Monte Carlo simulation was conducted to confirm and demonstrate the methodology.